Spaces of p-integrable functions with respect to a vector measure defined on a delta-ring

Abstract

[EN] The lattice properties of the Banach lattices Lp(m) and Lpw(m) of p-integrable real-valued functions and weakly p-integrable real-valued functions with respect to a vector measure m defined on a delta-ring are studied. The relation between these two spaces, the study of the continuity and some kind of compactness properties of certain multiplication operators between different spaces Lp and/or Lqw and the representation theorems of general Banach lattices via these spaces play a fundamental role.